I have a high pass and low pass filter, which look like this, R1 = 1kΩ R2 = 10kΩ , and C1 = 10 nF I need to find the breakpoint values for each of these filters. When I put them into LTSpice, it gives me 14.1kHz for the low pass filter, and 1.8kHz for the high pass filter. But when I use the equation 1/(2∏RC) to work out what the values should be ideally, it gives me something noticeably different. I know that this is because I'm not properly taking into account the second resistor, but I don't know how I to do this. How do I work out cutoff frequencies for filters in circuits with more than 1 resistor? thanks
If you add a load resistor Rload, then for the purpose of analysis R2 is replaced with Rload||R2. [ || meaning "in parallel with" ]
Sorry I guess I phrased my question badly, used terminology wrongly and whatnot, I'm very new to electronics in general. What I mean is, I don't know how to properly account for R2, because I've only ever seen examples of filters with 1 resistor.
Your question demonstrates the inadequacy of merely memorizing "formulas." Looking at case B, notice that we are seeking the voltage across R2, which is part of a basic voltage divider. Therefore: Dividing through by R2+R1, we get: Now we have separated the resistive component of the divider, which attenuates the signal regardless of frequency, from the reactive component, which IS dependent on frequency (note the presence of ω). Half power (cutoff) occurs when: Therefore, at cutoff: Solving for ω: Convert angular frequency to cyclical and you have your answer. This technique (NOT this formula) can be applied to part A as well.
so if I understand this right, which I probably dont, For the low pass filter, I need to find the parallel impedance of R2 and C1, like this... where z1 and z2 are r2 and c1 right? then put that into a voltage divider with R1, which gives I'm having trouble simplifying what I get at this point to anything meaningful though.
Actually, yes you do. Good work. Yes, it gets a bit tricky here. Try dividing through with Zp. Then expand Zp and continue simplifying from there. You should eventually end up with: